Problem: Solve for $x$ and $y$ using substitution. ${-x+y = -3}$ ${y = 4x+9}$
Since $y$ has already been solved for, substitute $4x+9$ for $y$ in the first equation. ${-x + }{(4x+9)}{= -3}$ Simplify and solve for $x$ $-x+4x + 9 = -3$ $3x+9 = -3$ $3x+9{-9} = -3{-9}$ $3x = -12$ $\dfrac{3x}{{3}} = \dfrac{-12}{{3}}$ ${x = -4}$ Now that you know ${x = -4}$ , plug it back into $\thinspace {y = 4x+9}\thinspace$ to find $y$ ${y = 4}{(-4)}{ + 9}$ $y = -16 + 9$ $y = -7$ You can also plug ${x = -4}$ into $\thinspace {-x+y = -3}\thinspace$ and get the same answer for $y$ : ${-}{(-4)}{ + y = -3}$ ${y = -7}$